Q. No.Consider a uniform electric field in the \(z\text-\)direction. The potential is constant:
a.
in all space
b.
for any \(x\) for a given \(z\)
c.
for any \(y\) for a given \(z\)
d.
on the \(x\text-y\) plane for a given \(z\)
1.
(a), (b), (c)
2.
(a), (c), (d)
3.
(b), (c), (d)
4.
(c), (d)
A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness \(d_1\) and dielectric constant \(K_1\) and the other has thickness \(d_2\) and dielectric constant \(K_2\), as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness \(d= d_1+d_2\) and effective dielectric constant \(K\). The \(K\) is:
| 1. | \(\frac{{K}_{1} {d}_{1}+{K}_{2} {d}_{2}}{{d}_{1}+{d}_{1}}\) | 2. | \(\frac{{K}_{1} {d}_{1}+{K}_{2} {d}_{2}}{{K}_{1}+{K}_{2}}\) |
| 3. | \(\frac{{K}_{1} {K}_{2}\left({d}_{1}+{d}_{2}\right)}{{K}_{1} {d}_{2}+{K}_{2} {d}_{1}}\) | 4. | \(\frac{2 {K}_{1} {K}_{2}}{{K}_{1}+{K}_{2}}\) |
| a. | the electric field is uniform |
| b. | the electric field is zero |
| c. | there can be no charge inside the region |
| d. | the electric field shall necessarily change if a charge is placed outside the region |
Choose the correct statement(s):
1. (b) and (c)
2. (a) and (c)
3. (b) and (d)
4. (c) and (d)
| 1. | can not be defined as \(-\int_{A}^{B} { \vec E\cdot \vec{dl}}\) |
| 2. | must be defined as \(-\int_{A}^{B} {\vec E\cdot \vec{dl}}\) |
| 3. | is zero |
| 4. | can have a non-zero value. |
The variation of electrostatic potential with radial distance \(r\) from the centre of a positively charged metallic thin shell of radius \(R\) is given by the graph:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Three charges, each \(+q\), are placed at the corners of an equilateral triangle \(ABC\) of sides \(BC\), \(AC\), and \(AB\). \(D\) and \(E\) are the mid-points of \(BC\) and \(CA\). The work done in taking a charge \(Q\) from \(D\) to \(E\) is:
| 1. | \(\frac{3qQ}{4\pi \varepsilon_0 a}\) | 2. | \(\frac{3qQ}{8\pi \varepsilon_0 a}\) |
| 3. | \(\frac{qQ}{4\pi \varepsilon_0 a}\) | 4. | \(\text{zero}\) |
| 1. | \(8\) along the negative \(X\text-\)axis |
| 2. | \(8\) along the positive \(X\text-\)axis |
| 3. | \(16\) along the negative \(X\text-\)axis |
| 4. | \(16\) along the positive \(X\text-\)axis |
If \(50~\text{J}\) of work must be done to move an electric charge of \(2~\text{C}\) from a point where the potential is \(-10\) volt to another point where the potential is \(\mathrm{V}\) volt, then the value of \(\mathrm{V}\) is:
1. \(5\) volt
2. \(-15\) volt
3. \(+15\) volt
4. \(+10\) volt
What is the area of the plates of a \(2~\text{F}\) parallel plate capacitor, given that the separation between the plates is \(0.5~\text{cm}\)?
1. \(1100~\text{km}^2\)
2. \(1130~\text{km}^2\)
3. \(1110~\text{km}^2\)
4. \(1105~\text{km}^2\)
The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:
| 1. | \(6~\mu\text{F}~\) | 2. | \(20~\mu\text{F} ~\) |
| 3. | \(3~\mu\text{F}~\) | 4. | \(10~\mu\text{F}\) |
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